MOTIVATION: Studying combinatorial patterns in cancer genomic datasets has recently emerged as a tool for identifying novel cancer driver networks. Approaches have been devised to quantify, for example, the tendency of a set of genes to be mutated in a 'mutually exclusive' manner. The significance of the proposed metrics is usually evaluated by computing P-values under appropriate null models. To this end, a Monte Carlo method (the switching-algorithm) is used to sample simulated datasets under a null model that preserves patient- and gene-wise mutation rates. In this method, a genomic dataset is represented as a bipartite network, to which Markov chain updates (switching-steps) are applied. These steps modify the network topology, and a minimal number of them must be executed to draw simulated datasets independently under the null model. This number has previously been deducted empirically to be a linear function of the total number of variants, making this process computationally expensive. RESULTS: We present a novel approximate lower bound for the number of switching-steps, derived analytically. Additionally, we have developed the R package BiRewire, including new efficient implementations of the switching-algorithm. We illustrate the performances of BiRewire by applying it to large real cancer genomics datasets. We report vast reductions in time requirement, with respect to existing implementations/bounds and equivalent P-value computations. Thus, we propose BiRewire to study statistical properties in genomic datasets, and other data that can be modeled as bipartite networks. AVAILABILITY AND IMPLEMENTATION: BiRewire is available on BioConductor at http://www.bioconductor.org/packages/2.13/bioc/html/BiRewire.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.